arXiv · arXiv · 2022
This paper describes multi-portfolio `internal' rebalancing processes used in the finance industry. Instead of trading with the market to `externally' rebalance, these internal processes detail how portfolio managers buy and sell between their portfolios to rebalance. We give an overview of currently used internal rebalancing processes, including one known as the `banker' process and another known as the `linear' pro…
Kelli Francis-Staite
arXiv · arXiv · 2026
The stability of markets hosting leveraged exchange-traded products is governed not by any single product's loop gain but by the spectral radius of a loop-gain matrix, and scalar per-product monitoring underestimates system feedback by construction. Recent work measures the self-reinforcement of a leveraged fund's daily close rebalancing through a scalar loop gain and treats cross-asset spillovers as bias. We model c…
Jihwan Woo
arXiv · arXiv · 2026
We present a simple framework for dynamic portfolio management that uses nothing but daily prices, trading volumes, and market capitalizations. Its state is three fixed-size matrices built from the price history: the distance matrix of the return correlations and the transition matrices of two Markov chains that rank the S\&P 500 names monthly by trailing return and by trailing volatility. These three matrices rest o…
Igor Halperin
arXiv · arXiv · 2010
The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C,…
Thomas Conlon, Heather J. Ruskin, Martin Crane
arXiv · arXiv · 2026
Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz…
Christian Bongiorno, Lorenzo Villassero
arXiv · arXiv · 2026
The Observable Matrix Dynamics (OMD) approach monitors the time development of complex non-linear systems through the trajectory of a fixed-size distance matrix and its spectrum. We apply it to the S\&P 500 cross section over three crisis decades, the 2001 dot-com bust, the 2007--2008 financial crisis, and the 2020 Covid crash, with three fixed-size observables on a fixed universe. The arccos distance matrix of the r…
Igor Halperin
arXiv · arXiv · 2026
This paper proposes a Structural Matrix Autoregressive (SMAR) model for the joint analysis of asset returns, realized volatility, and trading volume in a large-dimensional setting. This framework simultaneously captures dynamic spillovers across financial variables and cross-sectional dependence across assets while preserving a parsimonious parameterization relative to conventional vector autoregressive models. The m…
Andrea Bucci, Giulio Palomba, Eduardo Rossi
arXiv · arXiv · 2026
Return panels, covariances, and large feature matrices evolve one observation or one entry at a time, yet downstream models require an up-to-date low-rank factorization $A_t \approx U_t Σ_t V_t^\top$ on every tick -- a regime where full SVD is prohibitive and existing alternatives sacrifice either singular vectors, singular values, or long-horizon stability. We present a practical, metric-driven study of Brand-style …
Stilyan Staykov
arXiv · arXiv · 2026
We identify a robust structural signature of stock markets during exogenous shock events by analyzing collective return dynamics across G5 countries. Using Random Matrix Theory, we introduce the complexity gap, defined as the difference between the normalized largest eigenvalue and the average pairwise correlation, to quantify changes in market structure. This measure reveals a consistent three-phase pattern across m…
Kundan Mukhia, Imran Ansari, Md. Nurujjaman
arXiv · arXiv · 2026
We develop spectral portfolio theory by establishing a direct identification: neural network weight matrices trained on stochastic processes are portfolio allocation matrices, and their spectral structure encodes factor decompositions and wealth concentration patterns. The three forces governing stochastic gradient descent (SGD) - gradient signal, dimensional regularisation, and eigenvalue repulsion - translate direc…
Anders G Frøseth
arXiv · arXiv · 2025
We revisit Gerber's Informational Quality (IQ) framework, a data-driven approach for constructing correlation matrices from co-movement evidence, and address two obstacles that limit its use in portfolio optimization: guaranteeing positive semidefinite ness (PSD) and controlling spectral conditioning. We introduce a squeezing identity that represents IQ estimators as a convex-like combination of structured channel ma…
Layla Abu Khalaf, William Smyth
arXiv · arXiv · 2025
Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical interactions among assets. Motivated by this observation, we introduce a power-law covariance model to characterize collective market dynamics and propose a hybrid estimator that i…
Andres Garcia-Medina
arXiv · arXiv · 2024
We analyze correlation structures in financial markets by coarse graining the Pearson correlation matrices according to market sectors to obtain Guhr matrices using Guhr's correlation method according to Ref. [P. Rinn {\it et. al.}, Europhysics Letters 110, 68003 (2015)]. We compare the results for the evolution of market states and the corresponding transition matrices with those obtained using Pearson correlation m…
M. Mijaíl Martínez-Ramos, Parisa Majari, Andres R. Cruz-Hernández, Hirdesh K. Pharasi, Manan Vyas
arXiv · arXiv · 2022
We propose a portfolio allocation method based on risk factor budgeting using convex Nonnegative Matrix Factorization (NMF). Unlike classical factor analysis, PCA, or ICA, NMF ensures positive factor loadings to obtain interpretable long-only portfolios. As the NMF factors represent separate sources of risk, they have a quasi-diagonal correlation matrix, promoting diversified portfolio allocations. We evaluate our me…
Bruno Spilak, Wolfgang Karl Härdle
arXiv · arXiv · 2020
Multivariate volatility modeling and forecasting are crucial in financial economics. This paper develops a copula-based approach to model and forecast realized volatility matrices. The proposed copula-based time series models can capture the hidden dependence structure of realized volatility matrices. Also, this approach can automatically guarantee the positive definiteness of the forecasts through either Cholesky de…
Wenjing Wang, Minjing Tao
arXiv · arXiv · 2019
Using the United Nations COMTRADE database we apply the reduced Google matrix (REGOMAX) algorithm to analyze the multiproduct world trade in years 2004-2016. Our approach allows to determine the trade balance sensitivity of a group of countries to a specific product price increase from a specific exporting country taking into account all direct and indirect trade pathways via all world countries exchanging 61 UN COMT…
Célestin Coquidé, Leonardo Ermann, José Lages, D. L. Shepelyansky
arXiv · arXiv · 2018
We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary which also influences the …
Andreas Mühlbacher, Thomas Guhr
arXiv · arXiv · 2017
We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, cross-correlation matrices are calculated with a rolling window of 400 days. To quantify the volatile market stages where the potential risk is high, we apply t…
Tetsuya Takaishi